At the time,Defence Minister Linda Reynolds said the tribunal"did not present any new evidence that might support reconsideration of the valour inquiries recommendation".
The 18-year-old strapped himself to an anti-aircraft gun as the vessel went down and is credited with saving the lives of 49 crew during the height of World War II. He shot down at least one aircraft,before dying at his gun.
Mr Morrison said the VC was a"very serious award"and the government had a"very special responsibility to ensure that the integrity of the Victoria Cross is upheld for all those who have been honoured".
He said he had written to Governor-General David Hurley to recommend the late war hero receive the award.
"I am very pleased that the process that we have followed and we will be hopeful of what would come back as a contented response from Her Majesty,"Mr Morrison said.
"I have accepted these findings and I have so written in the support of higher recognition for Sheehan.